AN E120 CREW; DEPARTING SFO ON THE LUVVE TWO; WERE UNABLE TO CONTACT DEPARTURE BY LUVVE INTERSECTION; TURNED ON COURSE TO OSI TO THE CHAGRIN OF ATC.

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ON DEP FROM SFO ARPT OUR FLT PLAN CALLED FOR LUVVE2 DEP; WOODSIDE. WE TOOK OFF RWY 10L AND INTERCEPTED 120 DEG RADIAL OFF OF SFO VOR AS DEPICTED ON THE STAR. WHEN WE REACHED LUVVE INTERSECTION THE CTLR WAS REALLY BUSY AND WE HAD NOT RECEIVED A VECTOR TO CONTINUE PAST LUVVE INTERSECTION. THEREFORE WE PROCEEDED WITH OUR FLT PLAN AND TURNED TOWARDS WOODSIDE. AT THAT POINT THE CTLR ASKED IF WE WERE STILL HEADING ON A 120 DEG DIRECTION. WE RESPONDED NEGATIVE. 'WE ARE HEADING TOWARDS WOODSIDE.' THE CTLR INSTRUCTED US TO TURN LEFT HEADING 100 DEGS AND ALSO THAT WE SHOULD NOT HAVE TURNED TOWARDS WOODSIDE. THE COMBINATION OF HVY WORKLOAD FOR THE CTLR AND THE FACT THAT LUVVE INTERSECTION IS SO CLOSE TO THE ARPT DID NOT GIVE US ENOUGH TIME TO GET A WORD IN A BUSY FREQ TO ASK FOR A VECTOR AFTER LUVVE AND I BELIEVE THE SAME FACTORS CAUSED THE CTLR NOT TO GIVE US A VECTOR BY THE TIME WE REACHED THAT INTERSECTION. THAT LEFT US WITH THE DECISION OF CHOOSING A HEADING OF OUR OWN AFTER LUVVE INTERSECTION.